Suppose that 71% of diners ask for a manager when they have a complaint, while 29% of diners ask for a manager when they have a question about the menu. It is known that 44% of those that had a complaint felt the manager satisfied their problem, whereas 72% of those that had a menu question felt satisfied. A randomly diner felt satisfied following a managerial interaction. What is the probability that they were a diner with a complaint?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that 71% of diners ask for a manager when they have a complaint, while 29% of diners ask for a manager when they have a question about the menu. It is known that 44% of those that had a complaint felt the manager satisfied their problem, whereas 72% of those that had a menu question felt satisfied. A randomly diner felt satisfied following a managerial interaction. What is the probability that they were a diner with a complaint?
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Step 1

event

A : have complaint and ask for manager

B : gave question about the menu and ask for manager

C : ask for a manager and satisfied

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